It is often times desirable to determine the value of a contingent claim that may be exercised at some time in the future. The two most common forms of a contingent claim are a call and a put, both of which may arise in a wide variety of applications. For example, financial options commonly involve a call in which a stock or other financial instrument may be purchased at some time in the future for a predetermined exercise price or a put in which a stock or other financial instrument may be sold at some time in the future for a predetermined exercise price. While contingent claims frequently occur in the financial arena, contingent claims also arise in a number of other contexts, such as project evaluation and the evaluation of options to purchase or sell other assets, as described below. Unfortunately, the contingent claims that arise in these other contexts may be more difficult to evaluate than the contingent claims that arise in the financial context since the underlying assets in these other contexts are not traded or valued by a well established market, such as the stock market in the financial arena.
By way of example of the contingent claims that occur in contexts other than the financial arena, the contingent claims that arise during project evaluation and options to purchase or sell other assets will be hereinafter described. In this regard, a number of projects are structured so as to include a contingent claim that may be exercised by one of the participants at some time in the future. The contingent claim oftentimes comes in the form of a call in which one of the participants has an option to invest additional amounts of money in order to continue the project. As such, if the initial stages of the project have proved unsuccessful and/or if the future prospects for the project appear bleak, the participant capable of exercising the call will likely decline to invest additional money and thereby forego exercise of the call and will therefore terminate its participation in the project. Alternatively, if the initial stages of the project have been successful and/or if the prospects of success of the project are bright, the participant capable of exercising the call will likely make the necessary investment in order to continue its participation in the project.
The investment that guarantees continued participation will often take the formal financial form of a purchase of another call option. Concretely, the investment may be used to fund additional engineering and/or market research that continues the intermediate development of the technology or product. At these intermediate stages of development, there may not yet be sufficient confidence to commit to full-scale production, which may eventually proceed contingent on successful developmental progress, or, if unsuccessful, then termination of the effort. Therefore, funding for development may occur as a small, phased incremental stream of investments the values of which are calculated as a series of contingent claims. In sum, technology or product development can be modeled as a succession of call options.
Examples of projects that include a contingent claim at some subsequent time are widely varied, but one common example involves a project having a pilot phase extending from some initial time to a subsequent time at which the contingent claim may be exercised. If the contingent claim is exercised, such as by one of the participants contributing the necessary investment to the project, the project will enter a commercial phase. As a more specific example, the project may involve research and development having staged investments in which each investment is essentially a contingent claim with the participant opting to continue with the research and development activity if the participant makes sufficient progress and the necessary investment, but withdrawing from the research and development activity if the participant declines to make the investment.
By way of other specific examples, the contingent claim may represent an option for the participant to adjust its production level at a subsequent time or an option to adjust its production mix in the future. In such examples, not all the complete fabrication equipment or factory real estate is purchased at the onset of production, but rather as market demand proves strong, additional equipment is installed. The result is lowered risk in the face of uncertain market demand, which is offset by making a series of contingent, incremental investments. The difficult question is how to appropriately size and time investments balancing market uncertainty, the benefit of being well-equipped or the regret of having prematurely invested.
In addition to project analysis, contingent claims may arise in the context of contingent clauses in contractual agreements that may take advantage of incremental changes in performance contingent on specified anticipated future events. In such instances, shifts in delivery quantities or sales quotas can be set against a series of incremental investments or payments the amount of which is calculated as a multi-stage or compound option.
And in yet other scenarios, contingent claims may arise in the context of an option to purchase or sell assets other than financial assets. In such contexts, the contingent claim oftentimes comes in the form of a call or a put in which one of the participants purchases the contingent claim to thereby have an option to purchase an asset or sell an asset at some subsequent time for a predetermined exercise price. The asset in such contexts can comprise any of a number of different assets, both tangible and intangible assets, including goods, services, and licenses such as cruise ship tickets, tickets to the theatre or a sporting event, the rental of a hotel room, and the rental of a car. In a more specific example, then, the contingent claim may comprise an option to purchase an airline ticket with the option being purchased at some initial time, and the option capable of being exercised at a subsequent time to purchase the airline ticket.
In another similar example, the contingent claim may comprise an option to obtain a full refund on an asset purchased at some initial time, with the option being exercisable at a subsequent time to obtain a full refund. In a more specific example, the asset may comprise an airline ticket purchased at some initial time, where the airline ticket is purchased with an option to obtain a refund of the purchase price at a subsequent time at which the option may be exercised. If the option, or contingent claim, is exercised, the purchaser will then be able to obtain a refund of the purchase price of the ticket by selling the ticket back to the airline ticket vendor (e.g., airline).
Regardless of the type of contingent claim, it is desirable to determine the value of a project and, in particular, the contingent claim at the present time. By determining the value of the contingent claim, the participant can avoid overpaying for the project or asset as a result of an overvaluation of the contingent claim. Conversely, the participant can identify projects or assets in which the value of the contingent claim has been undervalued and can give strong consideration to investing in these projects or assets since they likely represent worthwhile investment opportunities. And although techniques have been developed for determining the value of a project or an asset having a contingent claim at one or more subsequent times, it is usually desirable to improve upon existing techniques.